Mister Exam

Lang:

Sum of series/ 10,2

Sum of series 10,2

The solution

You have entered [src]

$$\sum_{n=1}^{7} \frac{51}{5}$$

Sum(51/5, (n, 1, 7))

The rate of convergence of the power series

The answer [src]

357/5

$$\frac{357}{5}$$

357/5

Numerical answer [src]

71.4000000000000000000000000000

71.4000000000000000000000000000

The graph

Sum of series 10,2

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```